**Gas Laws and Kinetic Theory**

- This video discusses the different parameters of thermodynamics of gases like pressure, volume, temperature and mass at macro and micro level.
- The video explains the laws governing the relation between different parameters of the gases keeping one parameter constant at a time like Boyle’s law, Charles’ law, Gay- Lussac’s law, Avogadro’s law.
- This video explains the ideal gas equation involving pressure, volume, mass, temperature and a universal gas constant. It also illustrates the derivation of all other laws from this law only.
- Which of the following statements are true/false? Statement – 1: The figure shows the Volume-Temerature (V-T) graphs of a certain mass of an ideal gas at two pressures P1 and P2. It follows from the graphs that P1 is greater than P2. Statement – 2: The slope of V-T graph for an ideal gas is directly proportional to pressure.
- Which of the following statements are true/false? Statement-1: The figure shows PV/T versus Pressure (P) graph for a certain mass of oxygen gas at two temperatures T1 and T2. It follows from the graph that T1 > T2. Statement-2: At higher temperature, real gas behaves more like an ideal gas.
- A cylinder with known inside diameter contains air compressed by a piston of given mass, which can slide freely in the cylinder. The entire arrangement in immersed in a water bath whose temperature can be controlled. The system in initially in equilibrium at temperature T1 = 27 0C and initial height of the piston above the bottom of the cylinder is given. The temperature of the water bath is gradually increased to a final temperatureT2 = 77 0C. Calculate the height h2 of the piston. Starting from the same initial condition the temperature is again gradually raised, and weights are added to the piston to keep its height fixed at h1. Calculate the mass that has been added when the temperature has reached T2 = 77 0C.
- A vessel contains 1 mole of Oxygen gas (molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing one mole of Helium gas (molar mass 4) at a temperature 2T has pressure of….?
- A known mass of CO2 is contained in a vessel of known volume 5 and at a temperature. Assuming that 30% of the molecules are disassociated at this temperature, find the pressure of the gas.
- This video explains the assumption made to arrive at kinetic theory of gases which explains the behaviour of gases at microscopic level.
- This video explains the method to derive pressure and temperature of the gas by considering change in momentum and translational kinetic energy of gas particles at microscopic level respectively.
- Using the equation of pressure from Kinetic model, express Pressure in terms of a) Number Density b) Density of gas c) Number of moles and Molar mass.
- 1 L volume container contains a given mass of gas at a pressure, with mass of each gas particle known. Find the average translational kinetic energy of each particle.
- The pressure of a gas in a container is given along with average translational Kinetic energy of each gas particle. Find the number of gas particles in the container. How may moles are in the container?
- This video explains the method to derive mean free time and mean free path of the gas particle in term s of volume, average velocity and number of the particles if they are assumed to be spheres.
- This video explains the distribution of molecular speeds of the gas particles using Maxwell- Boltzmann probability distribution function. It also explains the probability density function for continuous distribution.
- This video explains the statistical distribution of molecular speeds of the gas particles in terms of room mean square speed, most probable speed and average speed using Maxwell- Boltzmann probability distribution function.
- Mark if the following statements are True or False. (a) The root-mean-square speed of the molecules of different ideal gases at the same temperature is the same. (b) The average translational kinetic energy of molecules of different ideal gases at the same temperature is the same.
- Three closed vessels A, B and C are at the same temperature. Vessel A Contains only Oxygen (O2), B only Nitrogen (N2) and C a mixture of equal quantities of oxygen and Nitrogen. If the average speed of O2 molecules in vessel A and that of N2 molecules in vessel B is known, the average speed of O2 molecules in vessel C will be…?
- At room temperature (27 0C) the root mean square (RMS) speed of the molecules of a certain diatomic gas is given. This gas is (a) H2 (b) F2 (c) O2 (d) Cl2
- Tell whether the following statement is true/false. The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.
- Tell whether the following statements are true/false. Statement 1: The root mean square speed (rms) of oxygen molecules (O2) at an absolute temperature T is known. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, the rms speed remains unchanged. Statement 2: The rms speed of the molecules of a gas is directly proportional to √(T/M) where M is the molar mass.
- The graph shows Maxwell velocity distribution for oxygen. (a) what will be the most probable speed of Nitrogen molecules at 600 K?
- This video illustrates the ways to deduce gas laws from the kinetic model of the gas. It also explains the Dalton’s law of partial pressure and Graham’s law of diffusion deduced from the kinetic properties of gas particles at molecular level.
- This video explains the molar heat capacities of gases at constant temperature and pressure and use of them in deriving adiabatic constant of the mono-atomic gases.
- This video explains the derivation of specific heat capacities and adiabatic constant for diatomic and polyatomic gases. It also explains the equipartition of energy based on the degrees of freedom of gas molecules.
- A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the mixture is…..?
- A vessel contains a mixture of 1 mole of oxygen and 1 mole of nitrogen at 300 K. The ratio of the rotational kinetic energy per mole of Oxygen (O2) to that per mole of Nitrogen(N2) is (a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) depends on the moment of inertia of the two molecules.
- Cv and Cp denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then which of the following is correct? (a) Cp - Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas (b) Cp + Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas(c) Cp/Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas (d) Cp . Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas
- This video explains the molar heat capacities at constant temperature and constant pressure along with adiabatic constant foe a mixture of two or more gases.
- One mole of a mono-atomic ideal gas is mixed with one mole of a diatomic ideal gas. (1) what will be the molar specific heat of the mixture at constant volume is (R = molar gas constant) (2) Find the adiabatic gas constant for the mixture if it is given for gases.
- The air density of Mount Everest is less than that at the sea level. It is found by mountaineers, that for one trip lasting a few hours, the extra oxygen needed by them corresponds to 30,000 cubic cm at sea level. If the temperature around Mount Everest and the capacity of oxygen cylinder, the pressure at which oxygen be filed (at site) in the cylinder is…?
- Two soap bubbles A and B are kept in a closed chamber where the air is maintained at a given pressure. If the radii of bubbles A and B and the surface tension of the soap water used to make bubbles is known, Find the ratio of the number of moles of air in bubbles A and B, respectively.
- A vertical hollow cylinder of given height is fitted with a movable piston of negligible mass thickness. The lower half portion of the cylinder contains an ideal gas and the upper half is filled with mercury. The cylinder is initially at 300 K. When the temperature is raised, half of the mercury comes out the cylinder. Find the temperature assuming the thermal expansion of mercury to be negligible.
- An electric bulb of known volume was sealed off during manufacture at a given pressure and temperature. Find the (a) number of molecules in the bulb. (b) number density of molecules (c) average distance between the molecules.
- A gaseous mixture at temperature T and pressure P containing helium and nitrogen has a density ρ. What is the concentration of helium and nitrogen in the given mixture?
- A jar contains a gas and few drops of water at given pressure and temperature. If the temperature of the jar is reduced by 1% and saturated vapour pressure at two temperatures is given, find the new pressure in the jar.
- A closed container of known volume contains a mixture of neon and argon gases at a given temperature and pressure. If the gram molecular weight of neon and argon and mass of total mixture is given, find the individual mass of the gases in container; assuming them to be ideal.
- During an experiment, an ideal gas is found to obey an additional law VP2 = constant. The gas is initially at temperature T and volume V. When it expands to a volume 2V, the temperature becomes….?
- Find the isothermal bulk modulus of an ideal gas kept at a given pressure and absolute temperature.
- An ideal gas is initially at temperature T and volume is increased by ΔV due to an increase in temperature ΔT, pressure remaining constant. Which of the following graphs correctly represents the variation of quantity δ = ΔV/(VΔT) with temperature?
- An ideal gas is expanding such that PT2 = constant. The coefficient of volume expansion of the gas is…?
- At what temperature, the root mean square speed of hydrogen (H2) molecules will be equal to escape velocity from earth’s surface? Given the radius of the earth and gas constant.
- Let Vavg, Vrms and Vp respectively denote the mean speed, root mean square speed and most probable speed of the molecules of an ideal mono-atomic gas at absolute temperature T. Then which of the following is correct? (a) Vp < Vavg < Vrms (b) the average kinetic energy of a molecule is (3/4) m Vp2 where m is mass of a molecule. (c) no molecule can have speed greater than √2 Vrms (d) no molecule can have speed less than Vp/ √2.
- Find the temperature at which (a) the root mean square velocity of oxygen molecules exceeds their most probable velocity by a given amount. (b) the most probable velocity of oxygen and nitrogen molecules differ by a certain amount.
- The average translational energy and the root mean square (rms) speed of molecules of a sample of oxygen gas at 300 K are known. The corresponding values at 600 K will be..? (assuming ideal gas behavior)
- Two mono-atomic ideal gases of molar masses M1 and M2 are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is ….?
- A pressure gauge indicates the differences between atmospheric pressure inside the tank, It shows two different reading; first at a given volume and second after some use. How many cubic meters of oxygen at normal atmospheric pressure were used? There is no temperature change during the time of consumption.
- An ideal gas has been placed in a tank at known temperature and pressure. One fourth of the gas is then released from the tank and thermal equilibrium is established. What will be the pressure if the temperature is given? Given standard atmospheric pressure.
- In a mercury barometer, some air is present in the space above the mercury, whose heights are given at two different reading of atmospheric pressures by it. The height of empty space is 60 mm. What is the true atmospheric pressure?
- Two glass bulb of known volume are connected to another of volume by means of a tube of negligible volume. The bulbs contain dry air and are both at a common temperature and pressure. The larger bulb is immersed in melting ice at 0 0C and the smaller in steam at 100 0C. Find the final common pressure.
- An ideal gas of given specific heat at constant pressure Cp is kept in a closed vessel at a known temperature and pressure. A given amount of heat energy is supplied to the gas. Calculate the final temperature and pressure of the gas.
- Under standard condition the density of an ideal gas is and the velocity of sound in it is known. How many degrees of freedom the gas molecules have?
- A gas consists of rigid diatomic molecules and is kept at a temperature T = 300 K. Find the angular root mean square velocity of rotating molecule if its moment of inertia is given.
- A container of volume Vc is evacuated by means of a piston pump. In each cycle the pump sucks in a volume Vp of air and expels it. The process is assumed to be isothermal, and the gas is ideal. The initial pressure inside the container is Po. What will be the final pressure inside the container after n cycles?
- Two ideal diatomic gases at absolute temperatures T1 and T2 are mixed with no loss of energy. Find the temperature of mixture if masses of molecules are m1 and m2 and the number of molecules in the gases are N1 and N2 respectively.
- One mole of oxygen at a given temperature is enclosed in a vessel which is moved with a constant speed and is then suddenly stopped, as a result the temperature of the gas rises by 1%. If the molecular mass of oxygen is given, find the adiabatic constant γ and velocity of the vessel with which it is moved.